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# M15-24

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:56
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Difficulty:

75% (hard)

Question Stats:

44% (01:01) correct 56% (01:17) wrong based on 114 sessions

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If points $$A$$, $$B$$, and $$C$$ form a triangle, is angle $$ABC \gt 90$$ degrees?

(1) $$AC = AB + BC - 0.001$$

(2) $$AC = AB$$
[Reveal] Spoiler: OA

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16 Sep 2014, 00:56
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Official Solution:

Statement (1) by itself is insufficient. We do not know the scale of the triangle. If 0.001 is small compared to the sides of the triangle then $$AC$$ almost equals $$AB + BC$$ and thus angle $$ABC$$ is obtuse. But if the sides are all small, 0.001 might not indicate that $$AC$$ is about equal to $$AB + BC$$.

Statement (2) by itself is sufficient. It means that $$\angle ABC = \angle BCA$$. A triangle cannot have two angles that are both greater than 90 degrees.

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Joined: 05 Jun 2012
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03 Dec 2014, 02:38
it is good question

stmt1 : clearly insufficient.

Stmt2 is sufficient to answer , suppose there are three angle x,y, and z , so x+y+z=180 , x=y

so 2y+z=180, value will be maximum when 2y=z , so 2z=180 zmax=90 , it can be greater than 90 (sufficient)
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Joined: 28 Mar 2014
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07 Oct 2015, 10:26
Statement 2 :- If triangle ABC is isosceles right angle triangle at B ...then statement B is inavalid...for rest other triangle it is valid

some time yes and sometime no

So answer will be E here i guess
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08 Oct 2015, 08:19
suyashtcs wrote:
Statement 2 :- If triangle ABC is isosceles right angle triangle at B ...then statement B is inavalid...for rest other triangle it is valid

some time yes and sometime no

So answer will be E here i guess

No, that's not correct. The second statement implies than angles B and C are equal and since a triangle cannot have two angles that are both greater than 90 degrees, then angle B must be less than 90 degrees.
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08 Oct 2015, 08:36
thankyou for nice explanation ....i was missing the key point...here
Senior Manager
Joined: 08 Jun 2015
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30 Jan 2017, 08:15
The answer must be option B.

First statement is just a re-statement of the in-equality theorem. Does not say anything about angle ABC.

Statement 2 on the other hand makes it clear that B can't be more than 90 if AC=AB. Hence the answer must be B.
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Joined: 12 Feb 2015
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30 Aug 2017, 11:10
Bunuel wrote:
Official Solution:

Statement (1) by itself is insufficient. We do not know the scale of the triangle. If 0.001 is small compared to the sides of the triangle then $$AC$$ almost equals $$AB + BC$$ and thus angle $$ABC$$ is obtuse. But if the sides are all small, 0.001 might not indicate that $$AC$$ is about equal to $$AB + BC$$.

Statement (2) by itself is sufficient. It means that $$\angle ABC = \angle BCA$$. A triangle cannot have two angles that are both greater than 90 degrees.

Hi Bunuel Sir,

Can you please explain A option via any example.I am not able to comprehend the explanation.
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Joined: 16 Jan 2013
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12 Dec 2017, 05:09
Pictorial explanation of statement 1 would be a great help

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31 Dec 2017, 07:10
hi bunuel...

pls can you explain st1 wrt this formulae:

c^2> a^2+b^2
Re: M15-24   [#permalink] 31 Dec 2017, 07:10
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# M15-24

Moderators: chetan2u, Bunuel

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